A365341 a(n) = (5*n)!/(4*n+1)!.

1, 1, 10, 210, 6840, 303600, 17100720, 1168675200, 93963542400, 8691104822400, 909171781056000, 106137499051584000, 13679492361575040000, 1929327666754295808000, 295570742023171270656000, 48877281133334949335040000, 8677556868736487617966080000

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: exp( 1/5 * Sum_{k>=1} binomial(5*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024

a(n) = A000142(n)*A002294(n). - Alois P. Heinz, Feb 08 2024

From Seiichi Manyama, Aug 31 2024: (Start)

E.g.f. satisfies A(x) = 1/(1 - x*A(x)^4).

a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * |Stirling1(n,k)|. (End)

Prog

(PARI) a(n) = (5*n)!/(4*n+1)!;
(Python)
from sympy import ff
def A365341(n): return ff(5*n, n-1) # Chai Wah Wu, Sep 01 2023

Crossrefs

Cf. A001761, A001763, A052795, A365340.

Cf. A004343.

Cf. A000142, A002294.

Sequence in context: A120596 A238467 A254322 * A327411 A112364 A201621

Adjacent sequences: A365338 A365339 A365340 * A365342 A365343 A365344

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 01 2023

Status

approved